WO2022257190A1

WO2022257190A1 - Quantum walk-based multi-feature simulation method for behavior trajectory sequences

Info

Publication number: WO2022257190A1
Application number: PCT/CN2021/102009
Authority: WO
Inventors: 俞肇元; 罗文�; 张季一; 袁林旺; 王增杰
Original assignee: 南京师范大学
Priority date: 2021-06-08
Filing date: 2021-06-24
Publication date: 2022-12-15
Also published as: CN113393488A

Abstract

A quantum walk-based multi-feature simulation method for behavior trajectory sequences, comprising the following steps: (1) generating a full set of feature sequences; (2) screening feature sequences; (3) constructing a feature sequence mapping mechanism; and (4) performing experimental verification. On the basis of transformation and combination characteristics between individual behaviors and group behaviors, feature structures of similar individuals are simulated from the perspective of multi-scale parsing by using quantum walks, and the simulation of behavior trajectories is achieved.

Description

A Multi-feature Simulation Method of Behavioral Trajectory Sequence Based on Quantum Walk

technical field

The invention relates to the technical fields of quantum mechanics and traffic geography, in particular to a multi-feature simulation method of a behavior trajectory sequence based on quantum walks.

Background technique

The development of big data, Internet of Things and precise positioning technology has promoted the progress of urban perception. With the increasing social activities, online car-hailing trajectory data not only records its driving trajectory, but also contains road traffic conditions, urban residents' travel patterns, urban structure and other social issues. The sequence of online car-hailing behavior trajectories is the aggregation result of behavior trajectories at different spatial and temporal scales, reflecting the state or degree of online car-hailing behavior trajectories changing over time at different spatial scales. Most of the current research on behavior trajectories focuses on the feature extraction and feature recognition of the trajectory data itself, seldom considers its structure and characteristics from the temporal and spatial distribution of behavioral trajectory sequences, and insufficient consideration is given to the spatiotemporal differentiation of behavioral trajectory sequences.

Based on data mining methods, the current research on behavior trajectory data mainly focuses on urban planning and social perception. In the direction of urban planning, behavioral trajectory data is mostly used to discover, identify and evaluate static urban planning and urban structure. For social perception, most scholars analyze and monitor the dynamic changes and movement patterns of crowd activities in cities based on behavior trajectory data. There have been more mature research results in the above two directions. In recent years, scholars in various fields have been trying to mine new knowledge and experience from behavior trajectory data, and have improved various theoretical methods, which can be classified into four categories: spatial statistics, time series methods, graph theory and complex networks. , and machine learning. Most of the above model methods carry out research work based on the behavior trajectory data itself, and have achieved fruitful research results, but there are few studies on the aggregated data of behavior trajectory.

Contents of the invention

The technical problem to be solved by the present invention is to provide a multi-feature simulation method of behavior trajectory sequence based on quantum walk, based on the transformation and combination characteristics between individual behavior and group behavior, using quantum walk to simulate similar individuals from the perspective of multi-scale analysis feature structure, and realize the simulation of behavior trajectory.

In order to solve the above-mentioned technical problems, the present invention provides a multi-feature simulation method of behavior trajectory sequence based on quantum walk, including the following steps:

(1) Generate a complete set of feature sequences;

(2) Screening feature sequences;

(3) Build a feature sequence mapping mechanism;

(4) Experimental verification.

Preferably, in step (1), generating the feature sequence of the complete set is specifically as follows: based on the basic assumption of quantum walk, in the inner city system gridded into m×n blocks, all possible distributions of behavioral features are defined as The ground state of the quantum walk is denoted as:

Indicates that the movement of the driver between different blocks is reflected in the transfer of particles between different nodes in the quantum walk simulation;

Define a Hilbert space H composed of ground states, and the superposition state formed by the linear combination of the ground states is also in this space; therefore, the state |δ(k)> of the quantum walk is defined as the linear superposition of all ground states :

where |a _i (k)|∈[0,1] represents the probability amplitude that the driver is in the state |i> at a given time; according to the assumption of randomness and based on unitary transformation, the state vector |δ(k)> is randomized The evolution over time is expressed as follows:

As shown in Equation (3), the dynamic evolution of the state vector depends on the adjacency matrix A, which is transformed into a matrix from the perspective of discrete points, and the state vector is effectively solved by matrix operations; so far, the ensemble feature based on quantum walk is constructed Sequence generation models.

Preferably, the parameters are constantly adjusted based on the following rules: 2000 quantum walks are performed on the 56 blocks in the research area, and the control parameters are increased from 0.01 to 20 with an interval of 0.01; finally, all possible The characteristic sequence of the quantum walk realizes the generation of the complete characteristic sequence of the quantum walk.

Preferably, in step (2), the screening feature sequence is specifically: use the ReliefF feature selection algorithm to screen the behavioral trajectory feature sequence, and under the constraints of the actual behavioral trajectory time sequence S, the complete set of feature sequences generated in step (1)

Perform ReliefF feature subset screening, which is expressed as:

Based on the weight of each feature, use the feature selection algorithm in Equation (4) to select from the ensemble feature sequence

Filter out N feature sequences with larger feature weights, denoted as

in

Preferably, four sets of feature sequence sets with different numbers are screened from the full set of feature sequences at one time according to the size of the feature weights, and the corresponding numbers of feature sequences are 5, 10, 20 and 30 respectively.

Preferably, in step (3), constructing a feature sequence mapping mechanism is specifically: based on step (2) screening the obtained modality

The aliasing coupling relationship between the behavior track sequence and the behavior mode is respectively established, and expressed as:

Preferably, in step (4), the experimental configuration in the experimental verification is specifically as follows: the research area is gridded into 0.01 ° x 0.01 ° blocks, a total of 56, and the network car-hailing every ten minutes in each block is counted Traffic time series, the length is 144, and the final processing obtains the required experimental data;

When generating the feature sequences of the complete set, 2000 quantum walks were carried out on the study area block, and its control parameters were increased from 0.01 to 20 at intervals of 0.01, and 5, 10, 20, and 30 feature sequences were selected for behavior trajectory sequences Carry out feature analysis and modeling simulation, and select the coefficient of determination ^R2 as the evaluation index, which is specifically defined as:

Among them, s _i is the actual behavior track sequence;

is the simulated behavior track sequence;

is the average value of the actual behavior trajectory sequence; l is the number of simulated samples.

The beneficial effects of the present invention are: the present invention analyzes the behavior track sequence from the perspective of multi-scale and multi-feature analysis, explores the coupling relationship between behavior track features and behavior track aggregation data, and constructs a robust multi-feature simulation of behavior track sequence method, and trying to apply it to intelligent transportation, resource and environmental protection, urban planning, social perception, etc., is a major breakthrough in the direction of behavioral trajectory modeling and simulation.

Description of drawings

Fig. 1 is a schematic flow chart of the method of the present invention.

Fig. 2 is a schematic diagram of the simulation results of the behavior track sequence of the five feature sequences of the present invention.

Fig. 3 is a schematic diagram of the simulation results of behavior track sequences of 10 feature sequences of the present invention.

Fig. 4 is a schematic diagram of the simulation results of behavior track sequences of 20 feature sequences of the present invention.

Fig. 5 is a schematic diagram of the simulation results of behavior track sequences of 30 feature sequences of the present invention.

Fig. 6 is a schematic diagram of the accuracy evaluation of the simulation results of the behavior trajectory sequence of the five feature sequences of the present invention.

Fig. 7 is a schematic diagram of the accuracy evaluation of the simulation results of the behavior trajectory sequence of the 10 feature sequences of the present invention.

Fig. 8 is a schematic diagram of the accuracy evaluation of the simulation results of the behavior trajectory sequence of 20 feature sequences in the present invention.

Fig. 9 is a schematic diagram of the accuracy evaluation of the simulation results of the behavior track sequence of 30 feature sequences in the present invention.

Detailed ways

As shown in Figure 1, a multi-feature simulation method for behavior trajectory sequences based on quantum walks includes the following steps:

(1) Generate a complete set of feature sequences;

(2) Screening feature sequences;

(3) Build a feature sequence mapping mechanism;

(4) Experimental verification.

In order to meet the basic assumption of quantum walk, the present invention abstracts drivers with the same or similar behavior trajectories as a class of quantized particles, then the movement process of such drivers on different grids can be described as the movement of particles between blocks In the transfer process, a class of behavior trajectories corresponds to a collapse of the quantized particle transfer process. When no observation is applied to the system, the particle will appear in multiple possible blocks with a certain probability, forming the dynamic evolution process of the probability of the particle appearing in each block over time, and then simulating the corresponding behavior trajectory sequence single character sequence.

However, the structure of behavioral trajectories within a city is complex, with strong heterogeneity among different regions, and it is difficult for a single feature sequence to represent the multimodal and complex structural characteristics of a behavioral trajectory sequence within a city. Therefore, considering the preparation of a full set of feature sequences with different structures and different oscillation characteristics is the "basis" for feature analysis and modeling of behavioral trajectory sequences. In terms of implementation, the quantum walk control parameter is the only parameter to generate a single feature sequence, which directly determines the structure of the feature sequence, that is, the structural characteristics of the corresponding probability distribution. Therefore, it is only necessary to continuously change the control parameters of the quantum walk to generate a complete set of feature sequences.

The movement process of drivers with the same or similar behavioral trajectories can be described as the transfer process of quantized particles between blocks in the study area, which is described by quantum walk. In the process of feature sequence generation, the key is that under the given parameters, the walker starts from the fixed block and performs quantum tour on the basic skeleton composed of the adjacency matrix (topological structure) of the research area after gridding. Go, forming the dynamic evolution of the probability distribution of behavioral characteristics over time under a single type of behavioral trajectory.

Based on the basic assumption of quantum walk, in the urban internal system gridded into m×n blocks, all possible distributions of behavioral characteristics can be defined as the ground state of quantum walk, which is denoted as:

It means that the movement of the driver between different blocks is reflected in the transfer of particles between different nodes in the quantum walk simulation.

In order to allow particles to dynamically adjust the probability of appearing in different blocks, a Hilbert space H composed of ground states is firstly defined, and the superposition state formed by the linear combination of ground states is also in this space. Therefore, the state |δ(k)> of the quantum walk can be defined as a linear superposition of all ground states:

where |a _i (k)|∈[0,1], represents the probability amplitude that the driver is in state |i> at a given time. Unlike classical random walks, quantum walks are not a Markov chain. According to the assumption of randomness, based on the unitary transformation, the evolution of the state vector |δ(k)> over time can be expressed as follows:

As shown in formula (3), the dynamic evolution of the state vector depends on the adjacency matrix A, and the differential equations containing complex coefficients are difficult to solve directly. Therefore, it is transformed into a matrix from the perspective of discrete points, and the state vector is efficiently solved by matrix operations. So far, a quantum walk-based ensemble feature sequence generation model has been constructed.

In the present invention, the parameters are constantly adjusted based on the following rules: 2000 quantum walks are performed on 56 blocks in the research area, and the control parameters are increased from 0.01 to 20 with an interval of 0.01. In the end, all possible feature sequences of 56 blocks were obtained, realizing the generation of the full set of feature sequences of quantum walks.

Although the internal behavior trajectory of the city is complex, subject to objective conditions, it is almost impossible for some ideal feature sequences to exist in the actual behavior trajectory sequence. Urban land use and functional zoning have improved the behavioral characteristics of the population and increased the heterogeneity of behavioral trajectory sequences between blocks, so the characteristic sequences on different blocks have certain differences. The ensemble feature sequence generated in step 1 is only a general set of feature sequences, and it does not yet have the ability to reveal the heterogeneity of behavior trajectories between different blocks. Therefore, under the constraints of the actual behavior trajectory sequence, based on specific feature sequence screening criteria, adaptive analysis can obtain the feature sequence set containing the behavior trajectory characteristics of a specific block. The mapping coupling relationship of behavior trajectory sequence lays the foundation.

The present invention uses the ReliefF feature selection algorithm to screen the behavior trajectory feature sequence, and under the constraints of the actual behavior trajectory time sequence S, the complete set of feature sequences generated by step (1)

To filter the subset of ReliefF features, it can be expressed as:

Filter out N feature sequences with larger feature weights, denoted as

in

In the present invention, four groups of feature sequence sets with different numbers are screened from the complete set of feature sequences at one time according to the feature weights, and the corresponding numbers of feature sequences are 5, 10, 20 and 30 respectively.

In the present invention, the feature sequence represents the probability that particles with the same or similar walking trajectories appear in different blocks, and there is a conversion mapping mechanism with the actual behavior trajectory sequence. Therefore, based on the eigenmodes of each block screened in step (2), the aliasing coupling relationship between the behavior trajectory sequence and the eigenmodes is established, and the mapping transformation from the simulated characteristic sequence to the actual behavior trajectory sequence is realized, and the fitting accuracy is achieved. Purpose.

Based on the obtained modes of step (2) screening

This invention adopts the local area of the Second Ring Road of Chengdu in November 2016 (104.04214°E-104.12214°E, 30.65294°N-30.72294°N, GCJ- 02 coordinate system) trajectory data as the original data. Data preprocessing is divided into two steps: first, the research area is gridded into 0.01°x0.01° blocks (56 in total), and then the time series of online car-hailing traffic every ten minutes in each block is counted (the length is 144), the final processing obtained the required experimental data.

When generating the feature sequence of the complete set, the present invention performs 2000 quantum walks on the research area block, and its control parameters are increased from 0.01 to 20 at intervals of 0.01. In order to explore the different granularity characteristics of the behavior track sequence, the present invention selects 5, 10, 20 and 30 feature sequences respectively to perform feature analysis and modeling simulation on the behavior track sequence. In order to compare and evaluate the effect of the simulation, the present invention selects the coefficient of determination (Coefficient of Determination, R ² ) as an evaluation index, which is specifically defined as:

Among them, s _i is the actual behavior track sequence;

is the simulated behavior track sequence;

Taking the time series of online car-hailing traffic every ten minutes in 56 blocks as the experimental data, the simulation experiment of the behavior trajectory sequence was completed. Figures 2-9 show the simulation results obtained by selecting 5, 10, 20 and 30 feature sequences and the accuracy evaluation of the simulation results, respectively. The results show that the five feature sequences can basically simulate the overall change trend of the behavior trajectory sequence, and the modeling accuracy is 0.6026-0.9524, which can reveal the dominant distribution structure of the behavior trajectory sequence in a day. However, the simulation effect of some blocks is relatively poor, such as N26, N40, and N49, and it is difficult to predict the fluctuations in the 0-48 period. This may be related to the spatial distribution of the stations, that is, there are few main roads near these three stations. Its characteristics are not revealed enough, and the simulation effect is relatively poor. In addition, the simulation results of the five characteristic sequences are still insufficient to capture the details, and it is difficult to reflect the high-frequency oscillation of the trajectory sequence. With the gradual increase of the characteristic sequence, the simulation effect is gradually improved, and the capture effect of the micro oscillation is also improved. The modeling accuracies of 10, 20 and 30 feature sequences are 0.6926-0.9494, 0.6926-0.9913, 0.6926-0.9966, respectively, and the modeling accuracy of some sites with simple behavior trajectory features is no longer affected by the number of feature sequences, indicating that the its characteristics and laws. Since this method is a data-driven method, the introduced feature sequences may have collinearity, and the simulation results also have overfitting problems. Therefore, it is necessary to further optimize the feature sequence screening rules and improve the mapping transformation mechanism between feature sequences and behavior trajectory sequences.

Claims

A quantum walk-based multi-feature simulation method for behavior trajectory sequences, characterized in that it comprises the following steps:

(1) Generate a complete set of feature sequences;

(2) Screening feature sequences;

(3) Build a feature sequence mapping mechanism;

(4) Experimental verification.
The multi-feature simulation method of behavior track sequence based on quantum walk as claimed in claim 1, characterized in that, in step (1), generating a full set of feature sequences is specifically: based on the basic assumption of quantum walk, in gridding as In the urban internal system of m×n blocks, all possible distributions of behavioral characteristics are defined as the ground state of the quantum walk, which is recorded as:

Indicates that the movement of the driver between different blocks is reflected in the transfer of particles between different nodes in the quantum walk simulation;

Define a Hilbert space H composed of ground states, and the superposition state formed by the linear combination of the ground states is also in this space; therefore, the state |δ(k)> of the quantum walk is defined as the linear superposition of all ground states :

where |a i (k)|∈[0,1] represents the probability amplitude that the driver is in the state |i> at a given time; according to the assumption of randomness and based on unitary transformation, the state vector |δ(k)> is randomized The evolution over time is expressed as follows:

As shown in Equation (3), the dynamic evolution of the state vector depends on the adjacency matrix A, which is transformed into a matrix from the perspective of discrete points, and the state vector is effectively solved by matrix operations; so far, the ensemble feature based on quantum walk is constructed Sequence generation models.
The multi-feature simulation method of behavior track sequence based on quantum walk as claimed in claim 2, characterized in that parameters are constantly adjusted based on the following rules: 2000 quantum walks are performed on 56 blocks in the research area, and its control parameters Increased from 0.01 to 20 with an interval of 0.01; finally, all possible feature sequences of 56 blocks were obtained, realizing the generation of the full set of feature sequences of quantum walks.
The behavioral trajectory sequence multi-feature simulation method based on quantum walk as claimed in claim 1, it is characterized in that, in step (2), screening characteristic sequence is specifically: screen behavioral trajectory characteristic sequence with ReliefF feature selection algorithm, in actual Under the constraints of the time series S of behavioral trajectories, the feature sequence of the complete set generated in step (1)
Perform ReliefF feature subset screening, which is expressed as:

Based on the weight of each feature, use the feature selection algorithm in Equation (4) to select from the ensemble feature sequence
Filter out N feature sequences with larger feature weights, denoted as
in
The multi-feature simulation method of behavior trajectory sequence based on quantum walk as claimed in claim 4, characterized in that, according to the feature weight size, four sets of feature sequence sets with different numbers are screened from the feature sequence of the complete set at one time, and the corresponding feature sequence numbers 5, 10, 20 and 30 respectively.
The multi-feature simulation method of behavior trajectory sequence based on quantum walk as claimed in claim 1, characterized in that, in step (3), constructing a feature sequence mapping mechanism is specifically: based on step (2) to screen the obtained modality
The aliasing coupling relationship between the behavior track sequence and the behavior mode is respectively established, and expressed as:
The multi-feature simulation method of behavior trajectory sequence based on quantum walk as claimed in claim 1, characterized in that, in step (4), the experimental configuration in the experimental verification is specifically: gridding the research area to 0.01 ° x0. There are 56 blocks at 01°, and the time series of online car-hailing traffic every ten minutes in each block is counted, the length is 144, and the required experimental data is finally processed;

When generating the feature sequences of the complete set, 2000 quantum walks were carried out on the study area block, and its control parameters were increased from 0.01 to 20 at intervals of 0.01, and 5, 10, 20, and 30 feature sequences were selected for behavior trajectory sequences Carry out feature analysis and modeling simulation, and select the coefficient of determination R2 as the evaluation index, which is specifically defined as:

Among them, s i is the actual behavior track sequence;
is the simulated behavior track sequence;
is the average value of the actual behavior trajectory sequence; l is the number of simulated samples.